anonymous
  • anonymous
Evaluate the determinants to verify the equation
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • anonymous
I have tried solving this and have been unsuccessful. Can anyone help me out?
JamesJ
  • JamesJ
is this your problem child of a problem?

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anonymous
  • anonymous
lol my problem
anonymous
  • anonymous
ummm the equation after the equal sign. Is that the determinant?
anonymous
  • anonymous
Since i know what the determinant equals but it doesnt equal that
JamesJ
  • JamesJ
it's asking you to evaluate the determinant and then show it does equal the expression on the RHS (right and side).
anonymous
  • anonymous
well it doesnt LOL
JamesJ
  • JamesJ
sure? I find the determinant to be \[ bc^3 + ca^3 + ab^3 - (ba^3 + cb^3 + ac^3) \]
anonymous
  • anonymous
ya i got that too
JamesJ
  • JamesJ
while the RHS, \[ RHS = (-a^2b + a^2c + ab^2 - ac^2 - b^2c + bc^2)(a+b+c) \] \[= ab^3 + bc^3 + ca^3 -(ba^3 - ac^3 - cb^3) \] which is the same.
JamesJ
  • JamesJ
in the brackets, should be + +
anonymous
  • anonymous
LOL I dont know where I went wrong but when I foiled I Landed up with too many cs
JamesJ
  • JamesJ
cs?
anonymous
  • anonymous
like the variable c
JamesJ
  • JamesJ
This problem is training you. Time to move beyond FOIL and multiply things out and keep track of them. Work this again and make sure you can replicate the result.
anonymous
  • anonymous
like what do u mean by moving beyond foil?
JamesJ
  • JamesJ
I mean you shouldn't need the rubric anymore. And what's more, you are seeing things with more than two terms in each bracket now. You should teach yourself to do that without using foil, a la the following (x + y + z)(a + b + c) = xa + xb + xc + ya + yb + yc + za + zb + zc
anonymous
  • anonymous
ya but like there it was (a-b)(b-c)(c-a)
anonymous
  • anonymous
so first i did (a-b)(b-c) and then i multiplied my answer by (c-a) Is that correct?
JamesJ
  • JamesJ
exactly so, that's equal to (ab - ac -b^2 + bc)(c-a) = abc - ac^2 -b^2c + bc^2 -a^2b+a^2c + ab^2 - abc = ab^2 + bc^2 + ca^2 - (ac^2 + ba^2 + ac^2)
JamesJ
  • JamesJ
etc., etc. Lots of ways to skin this cat. But having the discipline to work through it is important.
anonymous
  • anonymous
okkkkk i just caught my mistake LOL
JamesJ
  • JamesJ
ok, I'm going to move on.
anonymous
  • anonymous
You make one silly mistake and it ruins everything. Thanks James for ur help
JamesJ
  • JamesJ
Yes. Here's a hint for this problem. Clearly the problem is symmetric in a,b,c. Which means if we swapped the order of them it shouldn't upset the result too much. That being the case, at every step of the way, we should expect a certain symmetry in the terms. So if there's a term such as ab^2 it make sense that we should also expect a term such as bc^2 and ca^2 This is a way to at least sense check your answer at each step.
anonymous
  • anonymous
Alrighty Thanks for ur help :DDDDDDDD

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